高斯-勒让德公式 求积分

 1 #include <iostream>
 2 #include <cmath>
 3 using namespace std;
 4 //计算f(x)=1/x 在[1,3]上的积分
 5
 6 double f(double x){
 7     return 1.0/(x+2);
 8 }
 9
10 double f1(double x){
11     return 1.0/(x+5);
12 }
13 double f2(double x){
14     return 1.0/(x+7);
15 }
16
17 double f3(double x){
18     return 1.0/(x+9);
19 }
20 double f4(double x){
21     return 1.0/(x+11);
22 }
23
24 int main(){
25     //运用三点高斯公式积分值
26     printf("%2.8f\n",    (0.5555556*f( -0.7745967)+0.8888889*f( 0 )+0.5555556*f( 0.7745967) ));
27
28     //运用五点高斯公式求积分值
29     printf("%2.8f\n",  0.2369269*f(-0.9061799)+ 0.2369269*f(0.9061799)+0.4786287*f(-0.5384693)+0.4786287*f(0.5384693) +
30     0.5688889*f(0) );
31     printf("\n");
32
33     //将区间4等分，分别利用二点高斯公式，然后累加得积分值
34         printf("%2.8f\n",f1( -1.0/sqrt(3.0))+f1(1.0/sqrt(3.0))  );
35         printf("%2.8f\n",f2( -1.0/sqrt(3.0))+f2(1.0/sqrt(3.0))  );
36         printf("%2.8f\n",f3( -1.0/sqrt(3.0))+f3(1.0/sqrt(3.0))  );
37         printf("%2.8f\n",f4( -1.0/sqrt(3.0))+f4(1.0/sqrt(3.0))  );
38
39         printf("sum=%2.8f\n",f1( -1.0/sqrt(3.0))+f1(1.0/sqrt(3.0)) +f2( -1.0/sqrt(3.0))+f2(1.0/sqrt(3.0)) +f3( -1.0/sqrt(3.0))+f3(1.0/sqrt(3.0)) +f4( -1.0/sqrt(3.0))+f4(1.0/sqrt(3.0))  );
40
41 }